An orthogonal approach to the spatial-domain design of 2-D recursive and nonrecursive nonlinear filters

An orthogonal algorithm is used to design 2-D nonlinear filters which have spatial-domain representations as subsets of the general second-order 2-D nonlinear polynomial. This paper using these polynomial models, introduces a noniterative spatial-domain design technique to find the coefficients of the nonlinear filters. The method makes use of the Minimum Mean-Square Error (MMSE) criterion and allows for optimally reducing the number of non-zero coefficients in the filter model to meet a specified mean-square error. Furthermore, it guarantees a unique set of filter coefficients as the solution for a given filter structure. The algorithm is used to design recursive and nonrecursive nonlinear filters and it is shown that by introducing the recursive part, the filter performance is significantly improved.